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Fundamental group of the special orthogonal group SO(n)
Question: What is the fundamental group of the special orthogonal group SO(n) S O (n), n> 2 n> 2? Clarification: The answer usually given is: Z2 Z 2. But I would like to see a proof of that and …
Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · The generators of SO(n) S O (n) are pure imaginary antisymmetric n × n n × n matrices. How can this fact be used to show that the dimension of SO(n) S O (n) is n(n−1) 2 n …
Book recommendations for linear algebra - Mathematics Stack …
I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?
Boy Born on a Tuesday - is it just a language trick?
The following probability question appeared in an earlier thread: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? The claim was that it is not actual...
In a family with two children, what are the chances, if one of the ...
May 27, 2016 · For example, suppose there is a social science study on 2 child families with at least 1 daughter-- in this situation, about 1/3 of the families will be daughter-daughter, 1/3 will …
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s.
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
geometry - Find the coordinates of a point on a circle
I have a circle like so Given a rotation θ and a radius r, how do I find the coordinate (x,y)? Keep in mind, this rotation could be anywhere between 0 and 360 degrees. For example, I have a radiu...
Lie Algebra of U(N) and SO(N) - Mathematics Stack Exchange
Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the …
Are $SO(n)\\times Z_2$ and $O(n)$ isomorphic as topological …
Oct 19, 2019 · I am doing Exercise 4-16 in Armstrong's Basic Topology. The question is : are SO(n) ×Z2 S O (n) × Z 2 and O(n) O (n) isomorphic as topological groups? (I have proved the …
Universal covering group and fundamental group of $SO(n)$
If H H is a topological group which is both path-connected and locally path-connected (i.e. a connected Lie group such as SO(n) S O (n)), then any path-connected cover of H H inherits a …
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